Judith McKenna, the Walmart International CEO, told Asda managers at an event in Leeds, northern England, on Tuesday: "While we are not rushing into anything, I want you to know that we are seriously considering a path to an IPO - a public listing - to strengthen your long-term success."
But she cautioned that any preparations for an IPO would "take years", according to comments released by Asda afterwards.
Britain's competition regulator ruled Sainsbury's 7.3 billion pound ($9.4 billion) takeover of Asda could not proceed, blocking one potential exit route for Walmart from the UK.
The decision prompted analysts to speculate that Walmart would try to sell Asda to private equity or consider a stock market listing for the business, which it paid 6.7 billion pounds to acquire in 1999.
McKenna's comments are the first time Walmart has publicly addressed its future strategy for Asda since the Sainsbury's deal collapsed.
"Walmart does not have a one-size-fits-all approach to operating its international markets, but a consistent focus on strong local businesses powered by Walmart," she said.
Asda has reported seven consecutive quarters of like-for-like sales growth thanks to a strategy focused on lower prices, more innovation in own-brand products, better store standards and improvements in its e-commerce operations.
Monthly industry data produced by researcher Kantar indicates that Asda will likely report an eighth quarter of growth when it updates on trading on Thursday.
CEO Roger Burnley told managers at the Leeds meeting there would be 80 million pounds of price cuts throughout the rest of 2019.
Asda's strategy is working, he said, but noted it would be harder to deliver the strategy at the same pace without the synergies that the Sainsbury's deal would have provided.
(Reporting by James Davey; Editing by Sonya Hepinstall)